Group theory notes with complete explanation and examples

GROUP THEORY :

Group Theory, in Modern Algebra, the study of groups, which are systems consisting of a set of elements and a binary operation that can be applied to two elements of the set, which together satisfy certain axioms
These require that the group be closed under the operation (the combination of any two elements produces another element of the group), that it obey the associative law, that it contain an identity element (which, combined with any other element, leaves the latter unchanged), and that each element have an inverse (which combines with an element to produce the identity element). 
If the group also satisfies the commutative law, it is called a COMMUTATIVE, or ABELIAN, GROUP.
 The set of integers under addition, where the identity element is 0 and the inverse is the negative of a positive number or vice versa, is an Abelian GROUP.


































 MANUAL

RESEARCH PROJECT

B.Ed (1.5 Year/2.5 Year)

 

Course Code: 8613

Name:

Roll No.

Registration No.

Semester:

Region:

Theme: Work Ethics

Sub-Theme: Professionalism

Topic: The effect of professionalism in the development of student’s learning attitude at secondary level

 

 

 

 

 

 

 

 

  DECLARATION

(To be filled and signed by the student and retained by the Controller of Examination)

I ________________________________ Daughter / Son of __________________________

Roll No. _______________________________ Registration No. ______________________, a student of B.Ed Program (1.5 Year / 2.5 Year) at Allama Iqbal Open University do hereby declare that the research project entitled __________________________________________ ___________________________________________________________________________ submitted by me in partial fulfillment of B.Ed (1.5 Year / 2.5 Year) program is my original work and has not been submitted or published earlier. I also solemnly declare that it shall not, in future, be submitted for obtaining any other degree from this or any other university or institution.

I also understand the zero tolerance policy against plagiarism of the university and the HEC and if my work is found to be plagiarized or copied from someone other’s work at any stage, even after the award of the degree, the work may be cancelled and the degree confiscated.

_________________________________

          (Signature of the Student)

_________________________________

          (Name of the Student)

 

Date: _____________________

               (Day-Month-Year)

 

 

Research Project Submission Approval Form

(To be filled by the student; and signed by the supervisor and the RD)

This research project entitled ___________________________________________________ ___________________________________________________________________________ submitted by (student name) ____________________________________________________ Roll No. _______________________________ Registration No._______________________ Program (1.5 Year or 2.5 Year) ______________________ was conducted under my supervision. I have read it and found it to be satisfactory regarding its originality, content, language, relevancy, consistency, citation and reference list. It is ready for submission for evaluation to Allama Iqbal Open University as a partial fulfillment of B.Ed (1.5 Year / 2.5 Year).

____________________________

          (Signature of the Supervisor)

Date: ________________________

                      (Day-Month-Year)

       _____________________

            (Name of the Supervisor)

Certified that the student has completed at least 80% attendance and all required components of the workshop.

_______________________

(Signature of the Regional Director)

 

 

 

Name of the School (where the action research was conducted):

Action research was conducted in Government High School Lehri, Tehsil Sohawa, District Jhelum.

Overall background of the participants of the project; area/school: (socio-economic status, occupation/profession – earning trends of majority of the parents, literacy rate, academic quality, and any other special trait of the community where the school is situated) (10 marks)

Ø  Background of the Participants:

The participants of the study were class 10 students who were enrolled in Government High School Lehri, Tehsil Sohawa, District Jhelum. It involves one class consisting of 40 students. The research was conducted through teaching and learning in the school. I selected this school because I’m the teacher of that school. The students in this school faced different problems and study related stress. The socioeconomic background of the students was upper middle class. Most of them seem eager to study.  Their class room environment was not sufficient for effective learning. Most of their parents have middle economic level, so their study was not fully financially supported by their family.

Ø  School Area:

            Project School was Government High School Lehri, Tehsil Sohawa, District Jhelum. School building contains 24 classrooms. According to the school record, there are total of 450 students in numbers. The total staff of that school was 23. This school system has been appreciated by members of the nearby people, as well as by parents, teachers and other respective members of the community. Quran Majeed was taught since the third class. The school area belongs to the rural area. There is no computer lab and library for students. Separate playgrounds for upper and lower school students are located next to the upper and lower school buildings. Each classroom shows a list of school values, class rules and a blackboard that shows the learning structu